Math 1010-2 Midterm 2A
Name:
Instructions: There are TEN problems in this exam. Answer the questions in the spaces provided on the question sheets. If you need more space, use the bottom of the last page, but remember to indicate which problem you are doing. Partial credit will be awarded. Calculators are NOT allowed. This exam is closed book and closed notes. Show you work on each problem.
1. (10 points) Solve the following equation:
− x
2
+ 3 x − 3 = x
2. (10 points) Simplify the following expression:
5 x 3 y 2
10( xy − 1 ) 2
1

3. (10 points) Simplify the following complex fraction: x + 3 x + 5
1 x 2 − 25
4. (10 points) Rationalize the denominator of the following expression and simplify:
√
5 + 1
√
5 − 1
5. (10 points) Simplify the following product of polynomials by any method you choose:
( − x + x
2
+ 1)( x
2
+ x + 1)
Write your answer as a polynomial in standard form (i.e. from the highest power to the lowest).
2

6. (10 points) Factor the following polynomial: x
2 − 2 x − 15
7. (10 points) Solve the following equation by any method you choose: x −
√ x − 6 = 0
8. (10 points) Simplify the following radical expression:
√
3
5 x 4 +
√
3
40 x
3

9. (10 points) Evaluate the following expression so that no exponents appear in your final answer:
1
8
− 2
3
10. (10 points) (Golden Section) A point separates a line segment into two parts as in the following picture. Suppose the ratio between the length of the whole line segment and that of the left part is the same as the ratio between the left part and the right part. And suppose the length of the right part is 1. Find the length of the left part. (The ratio between a and b is a b
.) b b separation point b
4

Math 1010-2 Midterm 2B
Name:
Instructions: There are TEN problems in this exam. Answer the questions in the spaces provided on the question sheets. If you need more space, use the bottom of the last page, but remember to indicate which problem you are doing. Partial credit will be awarded. Calculators are NOT allowed. This exam is closed book and closed notes. Show you work on each problem.
1. (10 points) Solve the following equation:
− x
2
+ 3 x − 4 = x
2. (10 points) Simplify the following expression:
2 x 3 y 2
10( xy − 1 ) 2
1

3. (10 points) Simplify the following complex fraction: x + 3 x − 5
1 x 2 − 25
4. (10 points) Rationalize the denominator of the following expression and simplify:
√
5 − 1
√
5 + 1
5. (10 points) Simplify the following product of polynomials by any method you choose:
( − x + x
2
+ 1)( x
2
+ x + 1)
Write your answer as a polynomial in standard form (i.e. from the highest power to the lowest).
2

6. (10 points) Factor the following polynomial: x
2
+ 2 x − 15
7. (10 points) Solve the following equation by any method you choose: x +
√ x − 6 = 0
8. (10 points) Simplify the following radical expression:
√
3
5 x +
√
3
40 x 4
3

9. (10 points) Evaluate the following expression so that no exponents appear in your final answer:
1
9
− 3
2
10. (10 points) (Golden Section) A point separates a line segment into two parts as in the following picture. Suppose the ratio between the length of the whole line segment and that of the left part is the same as the ratio between the left part and the right part. And suppose the length of the right part is 1. Find the length of the left part. (The ratio between a and b is a b
.) b b separation point b
4